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Fermionic Formulas for Level-Restricted Generalized Kostka Polynomials and Coset Branching Functions |
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| Authors: | Anne Schilling Mark Shimozono |
| Affiliation: | Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA. E-mail: anne@math.mit.edu, US Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123, USA.?E-mail: mshimo@math.vt.edu, US |
| Abstract: | Level-restricted paths play an important r?le in crystal theory. They correspond to certain highest weight vectors of modules of quantum affine algebras. We show that the recently established bijection between Littlewood–Richardson tableaux and rigged configurations is well-behaved with respect to level-restriction and give an explicit characterization of level-restricted rigged configurations. As a consequence a new general fermionic formula for the level-restricted generalized Kostka polynomial is obtained. Some coset branching functions of type A are computed by taking limits of these fermionic formulas. Received: 9 April 2000 / Accepted: 26 January 2001 |
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